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Tyre characteristics and modelling 319 Table 5.5 Spline data for Interpolation model LATERAL FORCE (N) WITH SLIP ANGLE (DEG) AND LOAD (KG) SPLINE/100 ,X = -10,-8,-6,-4,-2,0,2,4,6,8,10 ,Y = 200,2148,2050,1806,1427,867,16,-912,-1508,-1881,-2067,-2151 ,Y = 400,3967,3760,3409,2727,1620,75,-1587,-2776,-3482,-3759,-3918 ,Y = 600,5447,5099,4436,3385,1962,94,-1893,-3397,-4557,-5049,-5269 ,Y = 800,6738,5969,4859,3533,2030,66,-1971,-3662,-5122,-6041,-6500 ALIGNING MOMENT (NM) WITH SLIP ANGLE (DEG) AND LOAD (KG) SPLINE/200 ,X = -10,-8,-6,-4,-2,0,2,4,6,8,10 ,Y = 200,4.6,-0.1,-6,-11.1,-10.9,-1.3,10.6,11.2,7.9,3.2,-0.3 ,Y = 400,-4.8,-19.6,-39,-52.1,-41.9,-6.7,35.8,49.1,38.6,23.4,10.1 ,Y = 600,-36.5,-73.1,-102.6,-107.9,-78.7,-14.2,60.6,96.2,93.4,65.8,40.7 ,Y = 800,-105.1,-181.1,-206.1,-172.4,-116.0,-3.6,79.9,143.3,172.2,141.5,98.5 LATERAL FORCE (N) WITH CAMBER ANGLE (DEG) AND LOAD (KG) SPLINE/300 ,X = -10,-8,-6,-4,-2,0,2,4,6,8,10 ,Y = 100,-123.3,-96.3,-64.6,-39.3,-3,19,46,80.6,108.3,146,173.3 ,Y = 200,-142.6,-106.6,-57.3,-14.6,28,78,127,169.6,212.3,255,285.6 ,Y = 300,-173.6,-106.6,-44,20.6,87.6,159,223.6,291.3,344.3,393.3,443.6 ,Y = 400,-194,-115.6,-31.3,53,141.6,237,319.6,396.3,468.6,526.3,579 ,Y = 500,-219.6,-121.6,-17.3,91,199,304,403.3,487,572.6,651.3,717 ,Y = 600,-247.6,-128.3,-9.3,109.3,234,351,453.3,557.3,651.6,734.6,829.6 ,Y = 700,-278,-138.6,-3.6,126.3,254,381,499.3,616,723,827,922.6 ,Y = 800,-318.6,-165,-21,128,261.3,404.0,524.3,656,780,895,1012 ALIGNING MOMENT (NM) WITH CAMBER ANGLE (DEG) AND LOAD (KG) SPLINE/400 ,X = -10,-8,-6,-4,-2,0,2,4,6,8,10 ,Y = 100,-5,-5,-4.3,-2.2,-0.9,1.2,2.6,4.2,5.8,7,6.4 ,Y = 200,-14.6,-13.7,-12,-9.2,-4.9,-0.9,3.6,6.7,9.6,11,11.7 ,Y = 300,-24.1,-22.6,-19.6,-16.7,-11.1,-4.2,2.8,8.1,11.9,15.2,17 ,Y = 400,-34.2,-31.8,-28.5,-22.9,-15.8,-8.2,-0.3,6.5,12.2,15.6,17.7 ,Y = 500,-41.5,-38,-32.7,-26.5,-18.8,-10.8,-2.5,3.9,10.7,16.5,19.6 ,Y = 600,-48.7,-43.6,-38,-31.6,-23.9,-15.9,-8.1,-0.4,6.4,12.1,16.8 ,Y = 700,-52.5,-47.5,-40.9,-34.4,-26.6,-19.5,-11.9,-4.7,1.3,7.2,12.6 ,Y = 800,-56.9,-51.3,-44.2,-37.9,-30.7,-23.9,-16.7,-10.1,-4,2.4,8.3 Table 5.6 Fiala tyre model parameters (average wheel load) R 1 318.5 mm R 2 97.5 mm k z 150 N/mm C s 110 000 N C 51 560 N/rad C 2580 N/rad C r 0.0 mm 0.05 0 1.05 1 1.05 Table 5.7 Fiala tyre model parameters (front wheel load) R 1 318.5 mm R 2 97.5 mm k z 150 N/mm C s 110 000 N C 54 430 N/rad C 2750 N/rad C r 0.0 mm 0.05 0 1.05 1 1.05
320 Multibody Systems Approach to Vehicle Dynamics Table 5.8 Fiala tyre model parameters (rear wheel load) R 1 318.5 mm R 2 97.5 mm k z 150 N/mm C s 110 000 N C 46 980 N/rad C 2350 N/rad C r 0.0 mm 0.05 0 1.05 1 1.05 Table 5.9 Lateral force ‘Magic Formula’ tyre model (version 3) parameters Aligning moment A0 .103370E01 C0 .235000E01 A1 .224482E05 C1 .266333E05 A2 .132185E01 C2 .249270E02 A3 .604035E05 C3 .159794E03 A4 .877727E04 C4 .254777E01 A5 0.0 C5 .142145E03 A6 .458114E04 C6 0.00 A7 .468222 C7 .197277E07 A8 .381896E06 C8 .359537E03 A9 .516209E02 C9 .630223 A10 0.00 C10 0.00 A11 .366375E01 C11 .120220E06 A12 .568859E02 C12 .275062E02 A13 0.00 C13 0.00 A14 0.00 C14 .172742E02 A15 0.00 C15 .544249E01 A16 0.00 C16 0.00 A17 .379913 C17 0.00 C18 0.00 C19 0.00 C20 0.00 5.9 Case study 6 – Comparison of vehicle handling tyre models Using the data derived from the tyre tests and the MSC.ADAMS tyre test rig the following plots have been produced here by way of example: (i) Lateral force for a range of plus and minus 10 degrees of slip angle (ii) Lateral force for a range of plus and minus 2 degrees of slip angle (near zero) For each plot a set of three curves is presented showing the variation in force or moment for each of the three tyre models. The comparisons are made separately at vertical loads of 200, 400, 600 and 800 kg. Using the Interpolation model as a benchmark the results plotted for the ‘Magic Formula’ and Fiala models are compared in Figures 5.72 to 5.79. The plots show that the more detailed ‘Magic Formula’ will produce a better match than the simpler Fiala model when examining the variation in lateral force with slip angle. Comparing the ‘Magic Formula’ with the
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Multibody Systems Approach to Vehic
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Multibody Systems Approach to Vehic
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Contents Preface Acknowledgements N
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Contents vii 4.10.1 Problem definit
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Contents ix 8.2.1 Active suspension
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Preface This book is intended to br
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Preface xiii vehicle design process
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Acknowledgements Mike Blundell In d
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Nomenclature xvii {z I } 1 Unit vec
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Nomenclature xix O n Frame for part
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Nomenclature xxi p Magnitude of re
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1 Introduction The most cost-effect
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Introduction 3 subsequent ‘classi
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Introduction 5 Fig. 1.4 Linearity:
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Introduction 7 While apparently a s
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Introduction 9 3. The body yaws (ro
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Introduction 11 Aspiration Definiti
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Introduction 13 Decomposition: Synt
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Introduction 15 The best multibody
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Introduction 17 shows good correlat
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Introduction 19 generated in numeri
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Introduction 21 1.9 Benchmarking ex
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2 Kinematics and dynamics of rigid
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Kinematics and dynamics of rigid bo
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3 Multibody systems simulation soft
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4 Modelling and analysis of suspens
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Modelling and analysis of suspensio
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Tyre characteristics and modelling
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7 Simulation output and interpretat
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Simulation output and interpretatio
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8 Active systems 8.1 Introduction M
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Active systems 443 mechanical actua
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Active systems 445 Table 8.1 MSC.AD
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Active systems 447 Body acceleratio
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Active systems 449 impressions of t
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Active systems 451 For this reason,
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Appendix A: Vehicle model system sc
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Appendix B: Fortran tyre model subr
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Appendix C: Glossary of terms Agili
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Appendix C: Glossary of terms 489 a
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Appendix C: Glossary of terms 491 t
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Appendix C: Glossary of terms 495 m
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Appendix C: Glossary of terms 499 t
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Appendix C: Glossary of terms 501 s
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References 503 Blundell, M.V. The m
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References 505 Hudi, J. AMIGO - A m
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References 507 Palmer, D. Course no
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References 509 European ADAMS News
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Index Abuse loads, 148 3 g bump, 14
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Index 513 Elk Test, 1 El-Nasher, 29
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Index 515 generalised translational
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Index 517 steer axis inclination, 1
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